“There may be ground for renewing that,’’ he said on ABC’s “This Week.”

And Mr. Blinken raised the idea of revising an agreement on the deployment of conventional forces in Europe that could keep military exercises far from borders — and thus reduce the fear that an exercise could become the leaping-off point for an invasion. “Those are certainly things that can be revisited if — if Russia is serious about doing it,” he said.

The Russians were incensed this fall when the United States and allied NATO forces conducted exercises in the Black Sea, near the Ukrainian and Russian coasts.

Privately, American officials have little hope that President Vladimir V. Putin of Russia would be satisfied with agreements that restore the status quo of a few years ago. And their concern is that the Russians will emerge from the Geneva talks, and others this week in Brussels and Vienna, declaring that diplomacy has failed — and that Mr. Putin will attempt to seize more of Eastern Ukraine, or carry out cyber or other attacks to cripple the government in Kyiv.

Still, Mr. Blinken’s statements appeared intended to create an opening, leaving the possibility of moving some heavy weaponry out of Poland, or limiting the scope of military exercises in Europe, in return for reciprocal actions by Russia — which presumably would have to include pulling troops back from the Ukraine border.

After a two-hour dinner with Ms. Sherman in Geneva Sunday evening, Mr. Ryabkov emerged sounding a slightly more positive tone. The talks were not “easy, but in principle, businesslike,” Mr. Ryabkov told reporters, adding, “I don’t think we will be wasting time tomorrow.”

Ms. Sherman did not comment publicly after the meeting, but the State Department released a statement saying she had told Mr. Ryabkov that the United States was committed to “sovereignty, territorial integrity and the freedom of sovereign nations to choose their own alliances,’’ pushing back on Moscow’s insistence that Ukraine never join the NATO alliance, and its threats to occupy more of the country than it seized in 2014.

The State Department said that on Monday it would take up “certain bilateral issues” with Russia, “but will not discuss European security without our European partners and allies.”